Method and apparatus for broadband mitigation of polarization mode dispersion

ABSTRACT

Described is a method and system for reducing system penalty from polarization mode dispersion. The method includes receiving a plurality of signals at a receiving end of a transmission line, each signal being received on one of a plurality of channels of the transmission line and measuring a signal degradation of at least one of the channels of the transmission line. An amount of adjustment of a polarization controller is determined based on the signal degradation, the amount of adjustment being selected to reduce the polarization mode dispersion. The amount of adjustment is then transmitted to the polarization controller.

BACKGROUND INFORMATION

Polarization mode dispersion is a limiting factor for high-speed, longhaul fiber optic communication. All network operators with highpolarization mode dispersion fiber or high bit rate long haul andultra-long-haul systems face this problem and network routes with olderfiber are particularly vulnerable. Due to its stochastic nature,polarization mode dispersion affects channels at random and varies intime. Many polarization mode dispersion compensation techniques havebeen explored. Each of these is categorized by two characteristics:location of the active mechanism and the number of channels mitigated bya single channel. So far, known compensation techniques are expensiveand cumbersome. It is therefore desirable to minimize outage probabilityof all channels in a cost efficient manner.

SUMMARY OF THE INVENTION

A method for reducing system penalty from polarization mode dispersion.The method includes receiving a plurality of signals at a receiving endof a transmission line, each signal being received on one of a pluralityof channels of the transmission line and measuring a signal degradationof at least one of the channels of the transmission line. An amount ofadjustment of a polarization controller is determined based on thesignal degradation, the amount of adjustment being selected to reducethe polarization mode dispersion. The amount of adjustment is thentransmitted to the polarization controller.

A system for polarization mode dispersion mitigation including atransmission line having a transmission end, a receiving end, and a spanlength, wherein the span length is a distance between the receiving endand the transmission end. A polarization controller is inserted into thetransmission line and a feedback channel connects the receiving end ofthe transmission line to the polarization controller to determine anamount of adjustment of the polarization controller based on a signaldegradation measure at the receiving end and transmit the amount ofadjustment to the polarization controller.

A polarization controller located in a transmission line having areceiving module to receive a feedback signal including an amount ofadjustment for the polarization controller, the amount of adjustmentbeing based on a signal degradation measured at a receiving end of thetransmission line and an adjusting module to adjust operation of thepolarization controller based on the feedback signal, wherein the amountof adjustment is selected to reduce the polarization mode dispersion.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an exemplary system according to the present invention.

FIG. 2 shows an exemplary method for reducing polarization modedispersion according to the present invention.

FIGS. 3 a-d shows exemplary results for three different feedback methodsusing a single mid-span polarization controller to reduce the outageprobability according to the present invention.

FIGS. 4 a-b show a PMD induced penalty CPF for a NRZ system with 25 and100 channels, respectively, using a mid-span polarization controlleraccording to the present invention.

FIG. 5 shows an exemplary polarization controller according to thepresent invention.

DETAILED DESCRIPTION

The present invention provides an apparatus and method to avoid thepolarization mode dispersion induced outages using a single polarizationcontroller and a low-bandwidth feedback loop. The invention pertains tothe field of long haul fiber optic telecommunications and describes theapparatus and method for broadband mitigation of the polarization modedispersion-induced system outages in a multi-channel telecommunicationsystem. The apparatus comprises at least one polarization controllerinserted into the transmission line at a location in the mid-span and afeedback signal based on the signal degradation measure of the worstchannel. The term mid-span should be understood to mean at any locationalong the transmission line from a transmission end to a receiving end.Preferable locations along the mid-span will be described in greaterdetail below. The apparatus also includes a feedback channel, which istypically available via the system supervisory channel. In oneembodiment, the feedback signal is the pre-FEC (Forward ErrorCorrection) bit error rate, and in yet another embodiment it is ameasure of depolarization of the optical signal, such as in astate-of-polarization (“SOP”) string length. Based on the values of thefeedback signal, the polarization controller is adjusted in order tominimize the feedback signal. Throughout this application, the termminimize is used to mean to reduce. For example, minimizing the feedbacksignal means to reduce the feedback signal from a current level. It doesnot necessarily mean that the feedback signal will be reduced to zero.

Referring to FIG. 1, there is shown an exemplary embodiment of a system100 according to the present invention. The system 100 includes anoptical transmission line 110 having a transmission end 120 with aplurality of transmitters 125 and a receiving end 130 with a pluralityof receivers 135. A plurality of signals may be transmitted from thetransmitters 125 to the receivers 135 via the transmission line 100. Aswould be understood by those of skill in the art, the plurality ofsignals may be transmitted simultaneously through the transmission line110 using a plurality of channels.

The system 100 typically includes a plurality of optical amplifiers 142,144 and 146 to amplify the signals as they are being transmitted throughthe transmission line 110. A polarization controller 150 is located at apoint preferably close to a ¼ of a span length from the transmitter 144.Throughout this description, the polarization controller is described asbeing located near a mid-span amplifier. It is not a requirement of thepresent invention that the polarization controller be in this location.However, numerical studies have indicated that this is the preferredplacement.

A feedback channel 170 connects the receiving end 130 of thetransmission line 110 to the polarization controller 150. A feedbacksignal is transmitted via the feedback channel 170 to adjust, preferablyon a continuous basis, the polarization controller 150. The feedbackchannel 170 made be made available via a system supervisory channel. Asdescribed above, the polarization controller is adjusted in order tominimize the feedback signal. Exemplary embodiments of the feedbacksignal will be described in greater detail below.

FIG. 2 shows an exemplary method 200 for reducing polarization modedispersion using the system 100 presented in FIG. 1. In step 210, aplurality of signals are transmitted through the transmission line 110via multiple channels. In step 220, characteristics of the signals aremeasured at the receiving end 130. As will be described below, differentcharacteristics may be measured to provide different feedback signalsused to adjust the polarization controller 150. In step 230, a feedbacksignal is generated based on the measured characteristic of the signals.In general, the feedback signal will be based on the measuredcharacteristics of the worst performing channel. However, as will bedescribed below, other channels or groups of channels may be selected togenerate the feedback signal.

The feedback signal is transmitted to the polarization controller 150via the feedback leap channel 170. As described above, the feedbackchannel 170 may be implemented via the system supervisory channel. Thepolarization controller 150 being preferably located at a ¼ span pointof the transmission line. In step 240, the polarization controller 150is adjusted based on the feedback signal to minimize the degradation ofthe signals. The method 200 may continue as long as signals are beingtransmitted through the transmission line 110 so that the step ofadjusting the polarization controller 150 may occur on a continuousbasis.

Thus, the present invention provides a broadband mitigation techniquewhich only requires a single low-bandwidth feedback signal going fromthe receiver side to the polarization controller which is preferablylocated at the ¼ span point. This compensation scheme is based on thefact that, for example, in a 100 channel system running at outageprobability of 10⁻⁵ per channel, there is approximately 10⁻³ probabilityof having an outage in one of the channels. In other words, only 0.1% ofthe fiber configuration space is bad for transmission. These bad spacesshould be avoidable using two degrees of freedom of a single mid-spanpolarization controller. A polarization controller is inserted close tothe mid-span and is continuously adjusted in order to minimize thesignal degradation of the worst performing channel (which may be SOPstring length or pre-FEC bit error rate), transmitted from the endreceiver.

In a typical telecom fiber link, the temporal evolution causespolarization mode dispersion of some channels to rise. The mid-span PMDmitigation technique and boundaries for its performance are described inmore detail below.

The fibers may be thought of as hundreds of birefringent piecesconnected by polarization rotators. Such a system as a whole has a largeconfiguration space, only one thousandth of which can cause an outage inone of the channels. By using a single mid-span polarization controller150, as shown in FIG. 1, to avoid bad regions of the parameter space,the outage probability can be reduced by orders of magnitude.

It is unexpected that any compensation technique which involvescommunication between parts that are not collocated would be desirable.However, given the relatively low cost of the present invention'smitigation technique, and its broadband nature, dedicating a part of thecontrol channel bandwidth to the polarization mode dispersion mitigationis a beneficial solution.

As described above, there are several characteristics of the signalsthat may be used to generate the feedback signal to control thepolarization controller 150. A first example may be the pre-FEC biterror rate, while a second example may be the polarization modedispersion itself (or a derivative thereof). The pre-FEC bit error rateis straightforward and is easy to measure for each channel. The feedbacksignal may be based on the pre-FEC signal for the worst channel.

There are several potential optimization functions that may be based onpolarization mode dispersion. First, is the polarization mode dispersionitself. The polarization mode dispersion measurement on a workingchannel is not straightforward, and requires at least two launchpolarizations to be used at every frequency, but can be done using thein-situ polarization techniques both at 10 and 40 Gb/s rates. Similar tothe technique described above, the feedback signal may be based on theworst channel polarization mode dispersion.

Second, the feedback signal may be based on the measurement of the meanpolarization mode dispersion of the channel by interferrometrictechniques, using the spectrum of the multiple channels. This techniqueis based on the assumption that the worst channels will be the keyinfluences on this value. Thus, minimizing the value will have the mosteffect on the worst channels. The minimization of this value may also bepotentially easier to obtain than the minimization of the worst channelpolarization mode dispersion.

Finally, it has been shown both theoretically and experimentally, thatthere is a good correlation between the PMD-induced system penalty andthe weighted length of the frequency-resolved SOP “string.” Thesestrings can be measured optically using polarization-resolvedspectrometry, or electrically, using heterodyne techniques. Theadvantage of this metric is that it does not require different launchSOP's at the input, and more importantly, it does not distinguishbetween low-polarization mode dispersion with bad SOP and highpolarization mode dispersion and the principal state launch. Thefeedback based on the optical properties of the signal, rather than thebit error rate has another advantage: it allows distinction betweenpolarization mode dispersion induced impairments and the signaldegradation caused by other processes, and allows a remedy to be chosenaccordingly.

In the following, the each of the above described feedback mechanismsbased on the polarization mode dispersion are considered and theirperformance is estimated, i.e., the minimization of the polarizationmode dispersion in the worst channel, the minimization of the meansquare value of the polarization mode dispersion, and the minimizationof the largest penalty across all channels is examined (e.g. SOPstring). Initially, the SOP string will be discussed. The outage can beestimated using an empirical expression in terms of themodulation-format-specific constant A, splitting ration y, and the ratioof DGD to the bit period τ/T:

$\begin{matrix}{{ɛ\left( \overset{->}{\tau} \right)} = {A\;{\gamma\left( {1 - \gamma} \right)}\left( \frac{\tau}{T} \right)^{2}}} & (1)\end{matrix}$which can be rewritten to relate to the orientation of the polarizationmode dispersion and SOP vector on the Stokes sphere as

$\begin{matrix}{{ɛ\left( \overset{->}{\tau} \right)} = {{\frac{A}{4\; T^{2}}\left( {{\overset{->}{\tau}}^{2}\sin^{2}\;\theta} \right)} = {\frac{A}{4\; T^{2}}\left( {{\overset{->}{\tau}}^{2} - \left( {\overset{->}{\tau} \cdot \overset{->}{S}} \right)^{2}} \right)}}} & (2)\end{matrix}$where θ is the angle between polarization mode dispersion and SOPvectors in the Stokes space. If the polarization string is defined as alength L_(s) of the polarization-resolved trace of the output SOP on thePoincare sphere, L_(s)=(τ/T)sin θ, where 1/T=10 GHz is the bandwidth ofthe signal, the equation reduces to

${ɛ\left( \overset{->}{\tau} \right)} = {\frac{{AL}_{S}^{2}}{4}.}$However, a more precise description of the penalty has been shown to be:

$\begin{matrix}{{ɛ\left( \overset{->}{\tau} \right)} = {\frac{{AL}_{S}^{2}}{4} + {BL}_{S}^{4}}} & (3)\end{matrix}$indicating that a SOP string is potentially a good estimator of thepolarization mode dispersion induced eye penalty. As described above,this measure is decoupled from the bit error rate performance which canbe affected by many other deleterious effects. The “string” measure ofpolarization mode dispersion does not reflect the effects ofpolarization-dependent chromatic dispersion. However this may be notcrucial, since, statistically, the second order polarization modedispersion is mostly orthogonal to the polarization mode dispersionvector.

The following considers a fiber with polarization mode dispersion τconsisting of two halves τ=τ₁Rτ₂ such that <τ₁ ²>=<τ₂ ²>=<τ²>/2.Assuming that rotation R is wavelength independent, and can beparameterized as R=exp({right arrow over (r)}×), with vector {rightarrow over (r)} denoting direction and angle of rotation. It is desiredto use the three available degrees of freedom in the rotation matrix Rin order to find the system-wide optimal position, that isτ_(max)=min_(R){max_(ω)|τ₁ +Rτ ₃|}  (4)and compare its distribution over the ensemble of channels to thedistribution of the worst channel's penalty that occurs withoutmitigation:

$\begin{matrix}{ɛ_{\max}^{0} = {\max\limits_{\omega}\left\{ {ɛ\left( {{\overset{->}{\tau}}_{1} + {\overset{->}{\tau}}_{2}} \right)} \right\}}} & (5)\end{matrix}$where it is assumed that there is no additional rotation for the secondhalf of the fiber. The distribution of τ_(max) [or ε_(max)] in anuncompensated system can be estimated analytically as F(ε)^(N), where Fis the corresponding cumulative distribution function for single channelPMD [or penalty] and N is the number or channels. Alternatively, themean square of the polarization mode dispersion can be minimized,looking therefore for the minimum of

$\begin{matrix}{\tau_{m\;{ax}}^{{rm}\; s} = {\min\limits_{R}{\left\{ \sqrt{\sum\limits_{\omega}\left( {\tau_{1} + {R\;\tau_{2}}} \right)^{2}} \right\}.}}} & (6)\end{matrix}$

Finally, the penalty can be minimized directly, looking therefore forthe minimum ofε_(max)=min_(R){max_(ω)ε(τ₁ +Rτ ₂)}.  (7)Given the arbitrary direction of polarization mode dispersion vectors inthis simulation, without loss of generality, the SOP of all channels isset to be the same, (1, 0, 0).

Next is considered the worst case scenario when all channels areindependent from each other, making the search for the global optimummore difficult. After the optimal position was found for each of thethree figures of merit above, the worst channel's penalty is computedusing the Eq. (1) for this position of the mid-span polarizationcontroller.

To test the above, simulations were run for two Non-Return-to-Zero(“NRZ”) systems, one with 25 channels (i.e. N=25) and another with 100channels (i.e. N=100), for a value of polarization mode dispersion ofτ_(rms)=0.2 T. In the simulations, empiric coefficients A=40 and B=40(see Eq. 3) were used to correspond to the Non-Return-to-Zero signal.Two hundred thousand (200000) fiber realizations were performed for eachsystem. Shown in FIGS. 3 a-d are the probability density function(“PDF”) and the cumulative probability function (“CPF”) for the penalty.The PDF and CDF of the worst channel's penalty in a system with 100statistically independent channels (FIGS. 3 a-b) and 25 statisticallyindependent channels. The worst channel is compared as is to threeoptimization methods: minimizing the maximum polarization modedispersion, minimizing the root mean square polarization modedispersion, and minimizing the maximum penalty.

One skilled in the art would recognize that the FIGS. 3 a-d illustratethe feasibility of using the various techniques described above forefficiently mitigating the polarization mode dispersion induced penaltyin a multi-channel system with a single polarization controller.Therefore, the polarization mode dispersion induced outages can bereduced by orders of magnitude. One can also see from the FIG. 3 thatthe feedback based on the direct estimation of the system penaltyprovides the best improvement in the system outage.

Further study of this polarization technique showed that even betterresults can be achieved if (i) better optimization algorithm is used and(ii) the polarization controller is placed at ¼ of the span from thetransmitter. The simulation supporting these results are presented inFIGS. 4 a-b for 25 and 100 channel systems, respectively. The simulationparameters are A=40, B=36 and τ_(rms)=0.18 T. The feedback is theoptical signal to noise ratio (“OSNR”) penalty. Initially, in FIG. 4 a,the PMD-induced penalty CPF in several cases for a wavelength divisionmultiplexing (“WDM”) system with 25 channels at 10 Gb/s is plotted. Thesolid line 410 refers to the unmitigated case. The dashed lines 420-450refer to simulations over 10⁵ realizations, with the polarizationcontroller at 0.75 span length (line 420), at the transmitter (line430), at 0.5 span length (line 440) and 0.25 span length (line 450).

Those skilled in art can see that the best performance is achieved whenthe polarization controller is located at ¼ of the span length. However,the performance improvement is still significant for the polarizationcontrollers located at the transmitter (e.g., at the transmission end ofthe transmission line) and at ½ of the span length.

FIG. 4 b shows the corresponding results for a system with 100 channels.Specifically, the solid line 460 refers to the unmitigated case. Thedashed lines 470-500 refer to simulations over 10⁵ realizations, withthe polarization controller at 0.75 span length (line 470), at thetransmitter (line 480), at 0.5 span length (line 490) and 0.25 spanlength (line 500).

FIG. 5 shows an exemplary embodiment of the polarization controller 150as described above with reference to FIG. 1. Those of skill in the artwill understand that the polarization controller 150 may be acombination of hardware and software adapted to perform the functionsdescribed above. The exemplary polarization controller 150 illustratedin FIG. 5 may include a receiving module 510 disposed to receivefeedback, such as that generated by the feedback channel 170 in step 230of the exemplary method 200. The polarization controller 150 may furtherinclude an adjusting module 520 for adjusting its polarization as perstep 240 of the method 200. Those of skill in the art will understandthat the receiving module 510 and the adjusting module 520 may becomprised of hardware, software, or a combination thereof.

The present invention has the advantages of overcoming the problemsassociated with typical compensation schemes. The system and method ofthe present invention allows for the fiber to “compensate itself”Furthermore, this method does not introduce any additional birefringentelements into the system. The present invention also has the operationaladvantage of providing predictable and potentially avoidable systemoutages on the physical layer. The present invention also provides thestrategic advantage of providing better use of existing fiber assets andcan serve as a base to more advances in distributed polarization modedispersion mitigation techniques.

It will be apparent to those skilled in the art that variousmodifications may be made in the present invention, without departingfrom the spirit or scope thereof. Thus, it is intended that the presentinvention cover the modifications and variations of this inventionprovided they come within the scope of the appended claims and theirequivalents.

1. A method for reducing system penalty from polarization modedispersion, comprising: receiving a plurality of signals at a receivingend of a transmission line, each signal being received on one of aplurality of channels of the transmission line; measuring a signaldegradation of each of more than one of the channels of the transmissionline; identifying a worst one of the measured signal degradations;determining an amount of adjustment of a polarization controller basedon the worst one of the measured signal degradations, the amount ofadjustment being selected to reduce the polarization mode dispersion;and transmitting the amount of adjustment to the polarizationcontroller, wherein the signal degradation is a polarization modedispersion, and wherein the amount of adjustment is determined based ona weighted length of a frequency-resolved state-of-polarization string.2. The method of claim 1, wherein the polarization controller is locatedsubstantially at ¼ of a span length from a transmission end of thetransmission line.
 3. The method of claim 1, wherein the amount ofadjustment is transmitted in a feedback signal.
 4. The method of claim3, wherein the feedback signal is transmitted via a feedback channelmade available via a system supervisory channel of the transmissionline.
 5. The method of claim 1, wherein the weighted length is measuredoptically.
 6. A system for polarization mode dispersion mitigation,comprising: a transmission line having a transmission end, a receivingend, and a span length, wherein the span length is a distance betweenthe receiving end and the transmission end; a polarization controllerinserted into the transmission line; and a feedback channel connectingthe receiving end of the transmission line to the polarizationcontroller to relay a measured signal degradation of each of a pluralityof channels of the transmission line, the receiving end identifying aworst one of the measured signal degradations, determining an amount ofadjustment of the polarization controller based on the worst one of themeasured signal degradations, and transmitting the amount of adjustmentto the polarization controller, wherein the signal degradation is apolarization mode dispersion, and wherein the amount of adjustment isdetermined based on a weighted length of a frequency-resolvedstate-of-polarization string.
 7. The system of claim 6, wherein theamount of adjustment is transmitted in a feedback signal.
 8. The systemof claim 7, wherein the feedback signal is transmitted via a systemsupervisory channel of the system.
 9. The system of claim 6, wherein thepolarization controller is inserted at substantially ¼ of the spanlength from the transmission end.
 10. The system of claim 6, wherein theweighted length is measured optically.
 11. A polarization controllerlocated in a transmission line, comprising: a receiving module toreceive a feedback signal including an amount of adjustment for thepolarization controller, the amount of adjustment being based on asignal degradation measured at a receiving end of the transmission line,wherein the transmission line has a plurality of channels and the signaldegradation of each channel is measured to create the feedback signal,wherein the feedback signal is based on a channel of the transmissionline with a largest amount of signal degradation; and an adjustingmodule to adjust operation of the polarization controller based on thefeedback signal, wherein the amount of adjustment is selected to reducethe polarization mode dispersion, wherein the signal degradation is apolarization mode dispersion, and wherein the amount of adjustment isdetermined based on a weighted length of a frequency-resolvedstate-of-polarization string.
 12. The polarization controller of claim11, wherein the feedback signal is received via a feedback channelimplemented in a system supervisory channel of the transmission line.13. The polarization controller of claim 11, wherein the polarizationcontroller is located at substantially ¼ of a span length of thetransmission line, the span length being equal to a distance from atransmission end to the receiving end of the transmission line.
 14. Thepolarization controller of claim 11, wherein the feedback signal is ameasure of depolarization.
 15. The polarization controller of claim 11,wherein the weighted length is measured optically.